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  {
   "cell_type": "markdown",
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   "source": [
    "# Stitch Two Networks with Different Spacing\n",
    "\n",
    "This tutorial explains how to use the stitch function to not only combine two networks into a single domain, but to have OpenPNM automatically creat throats between the two domains based on the spatial proximity of pores on each network.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:57.695512Z",
     "iopub.status.busy": "2021-06-24T11:31:57.693769Z",
     "iopub.status.idle": "2021-06-24T11:31:58.415712Z",
     "shell.execute_reply": "2021-06-24T11:31:58.414068Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import openpnm as op\n",
    "%config InlineBackend.figure_formats = ['svg']\n",
    "import openpnm.models.geometry as gm\n",
    "import openpnm.models.physics as pm\n",
    "import openpnm.models.misc as mm\n",
    "import matplotlib.pyplot as plt\n",
    "np.set_printoptions(precision=4)\n",
    "np.random.seed(10)\n",
    "ws = op.Workspace()\n",
    "ws.settings[\"loglevel\"] = 40\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate Two Networks with Different Spacing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.422735Z",
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     "shell.execute_reply": "2021-06-24T11:31:58.426742Z"
    }
   },
   "outputs": [],
   "source": [
    "spacing_lg = 0.00006\n",
    "layer_lg = op.network.Cubic(shape=[10, 10, 1], spacing=spacing_lg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
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    }
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   "outputs": [],
   "source": [
    "spacing_sm = 0.00002\n",
    "layer_sm = op.network.Cubic(shape=[30, 5, 1], spacing=spacing_sm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Position Networks Appropriately, then Stitch Together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.461597Z",
     "iopub.status.busy": "2021-06-24T11:31:58.454119Z",
     "iopub.status.idle": "2021-06-24T11:31:58.466057Z",
     "shell.execute_reply": "2021-06-24T11:31:58.464828Z"
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   "outputs": [],
   "source": [
    "# Start by assigning labels to each network for identification later\n",
    "layer_sm.set_label(\"small\", pores=layer_sm.Ps, throats=layer_sm.Ts)\n",
    "layer_lg.set_label(\"large\", pores=layer_lg.Ps, throats=layer_lg.Ts)\n",
    "# Next manually offset CL one full thickness relative to the GDL\n",
    "layer_sm['pore.coords'] -= [0, spacing_sm*5, 0]\n",
    "layer_sm['pore.coords'] += [0, 0, spacing_lg/2 - spacing_sm/2]  # And shift up by 1/2 a lattice spacing\n",
    "# Finally, send both networks to stitch which will stitch CL onto GDL\n",
    "from openpnm.topotools import stitch\n",
    "stitch(network=layer_lg, donor=layer_sm,\n",
    "       P_network=layer_lg.pores('back'),\n",
    "       P_donor=layer_sm.pores('front'),\n",
    "       len_max=0.00005)\n",
    "combo_net = layer_lg\n",
    "combo_net.name = 'combo'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quickly Visualize the Network\n",
    "Let's just make sure things are working as planned using OpenPNMs basic visualization tools:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2021-06-24T11:31:58.706087Z"
    }
   },
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   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "fig, ax = plt.subplots(figsize=[5, 5])\n",
    "op.topotools.plot_connections(network=combo_net, ax=ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Geometry Objects for Each Layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.714496Z",
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     "shell.execute_reply": "2021-06-24T11:31:58.718317Z"
    }
   },
   "outputs": [],
   "source": [
    "Ps = combo_net.pores('small')\n",
    "Ts = combo_net.throats('small')\n",
    "geom_sm = op.geometry.GenericGeometry(network=combo_net, pores=Ps, throats=Ts)\n",
    "Ps = combo_net.pores('large')\n",
    "Ts = combo_net.throats('small', mode='not')\n",
    "geom_lg = op.geometry.GenericGeometry(network=combo_net, pores=Ps, throats=Ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Add Geometrical Properties to the *Small* Domain\n",
    "The *small* domain will be treated as a continua, so instead of assigning pore sizes we want the 'pore' to be same size as the lattice cell. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.729038Z",
     "iopub.status.busy": "2021-06-24T11:31:58.727780Z",
     "iopub.status.idle": "2021-06-24T11:31:58.740978Z",
     "shell.execute_reply": "2021-06-24T11:31:58.739674Z"
    }
   },
   "outputs": [],
   "source": [
    "geom_sm['pore.diameter'] = spacing_sm\n",
    "geom_sm['pore.area'] = spacing_sm**2\n",
    "geom_sm['throat.diameter'] = spacing_sm\n",
    "geom_sm['throat.area'] = spacing_sm**2\n",
    "geom_sm['throat.length'] = 1e-12  # A very small number to represent nearly 0-length\n",
    "geom_sm.add_model(propname='throat.endpoints',\n",
    "                  model=gm.throat_endpoints.spherical_pores)\n",
    "geom_sm.add_model(propname='throat.length',\n",
    "                  model=gm.throat_length.piecewise)\n",
    "geom_sm.add_model(propname='throat.diffusive_size_factors',\n",
    "                  model=gm.diffusive_size_factors.spheres_and_cylinders)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Add Geometrical Properties to the *Large* Domain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.752315Z",
     "iopub.status.busy": "2021-06-24T11:31:58.750808Z",
     "iopub.status.idle": "2021-06-24T11:31:58.763791Z",
     "shell.execute_reply": "2021-06-24T11:31:58.764884Z"
    }
   },
   "outputs": [],
   "source": [
    "geom_lg['pore.diameter'] = spacing_lg*np.random.rand(combo_net.num_pores('large'))\n",
    "geom_lg.add_model(propname='pore.area',\n",
    "                  model=gm.pore_cross_sectional_area.sphere)\n",
    "geom_lg.add_model(propname='throat.diameter',\n",
    "                  model=mm.from_neighbor_pores,\n",
    "                  prop='pore.diameter', mode='min')\n",
    "geom_lg.add_model(propname='throat.area',\n",
    "                  model=gm.throat_cross_sectional_area.cylinder)\n",
    "geom_lg.add_model(propname='throat.endpoints',\n",
    "                  model=gm.throat_endpoints.spherical_pores)\n",
    "geom_lg.add_model(propname='throat.length',\n",
    "                  model=gm.throat_length.piecewise)\n",
    "geom_lg.add_model(propname='throat.diffusive_size_factors',\n",
    "                  model=gm.diffusive_size_factors.spheres_and_cylinders)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Phase and Physics Objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.777345Z",
     "iopub.status.busy": "2021-06-24T11:31:58.775947Z",
     "iopub.status.idle": "2021-06-24T11:31:58.782165Z",
     "shell.execute_reply": "2021-06-24T11:31:58.781005Z"
    }
   },
   "outputs": [],
   "source": [
    "air = op.phases.Air(network=combo_net, name='air')\n",
    "phys_lg = op.physics.GenericPhysics(network=combo_net, geometry=geom_lg, phase=air)\n",
    "phys_sm = op.physics.GenericPhysics(network=combo_net, geometry=geom_sm, phase=air)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add pore-scale models for diffusion to each Physics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.788886Z",
     "iopub.status.busy": "2021-06-24T11:31:58.787638Z",
     "iopub.status.idle": "2021-06-24T11:31:58.799861Z",
     "shell.execute_reply": "2021-06-24T11:31:58.800941Z"
    }
   },
   "outputs": [],
   "source": [
    "phys_lg.add_model(propname='throat.diffusive_conductance',\n",
    "                  model=pm.diffusive_conductance.ordinary_diffusion)\n",
    "phys_sm.add_model(propname='throat.diffusive_conductance',\n",
    "                  model=pm.diffusive_conductance.ordinary_diffusion)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the *small* layer we've used a normal diffusive conductance model, which when combined with the diffusion coefficient of air will be equivalent to open-air diffusion.  If we want the *small* layer to have some tortuosity we must account for this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.807505Z",
     "iopub.status.busy": "2021-06-24T11:31:58.806080Z",
     "iopub.status.idle": "2021-06-24T11:31:58.808998Z",
     "shell.execute_reply": "2021-06-24T11:31:58.810107Z"
    }
   },
   "outputs": [],
   "source": [
    "porosity = 0.5\n",
    "tortuosity = 2\n",
    "phys_sm['throat.diffusive_conductance'] *= (porosity/tortuosity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that this extra line is NOT a pore-scale model, so it will be over-written when the `phys_sm` object is regenerated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Add a Reaction Term to the Small Layer\n",
    "A standard n-th order chemical reaction is $ r=k \\cdot x^b $, or more generally: $ r = A_1 \\cdot x^{A_2} + A_3 $.  This model is available in `OpenPNM.Physics.models.generic_source_terms`, and we must specify values for each of the constants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.816868Z",
     "iopub.status.busy": "2021-06-24T11:31:58.816099Z",
     "iopub.status.idle": "2021-06-24T11:31:58.819919Z",
     "shell.execute_reply": "2021-06-24T11:31:58.820497Z"
    }
   },
   "outputs": [],
   "source": [
    "# Set Source Term\n",
    "air['pore.A1'] = -1e-10  # Reaction pre-factor\n",
    "air['pore.A2'] = 1  # Reaction order\n",
    "air['pore.A3'] = 0  # A generic offset that is not needed so set to 0\n",
    "phys_sm.add_model(propname='pore.reaction',\n",
    "                  model=pm.generic_source_term.power_law,\n",
    "                  A1='pore.A1', A2='pore.A2', A3='pore.A3',\n",
    "                  X='pore.concentration', \n",
    "                  regen_mode='deferred')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform a Diffusion Calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:58.833981Z",
     "iopub.status.busy": "2021-06-24T11:31:58.833104Z",
     "iopub.status.idle": "2021-06-24T11:31:58.987373Z",
     "shell.execute_reply": "2021-06-24T11:31:58.987987Z"
    }
   },
   "outputs": [],
   "source": [
    "Deff = op.algorithms.ReactiveTransport(network=combo_net, phase=air)\n",
    "Ps = combo_net.pores(['large', 'front'], mode='intersection')\n",
    "Deff.set_value_BC(pores=Ps, values=1)\n",
    "Ps = combo_net.pores('small')\n",
    "Deff.set_source(propname='pore.reaction', pores=Ps)\n",
    "Deff.settings['conductance'] = 'throat.diffusive_conductance'\n",
    "Deff.settings['quantity'] = 'pore.concentration'\n",
    "Deff.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the Concentration Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the result would look something like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-06-24T11:31:59.012551Z",
     "iopub.status.busy": "2021-06-24T11:31:59.007844Z",
     "iopub.status.idle": "2021-06-24T11:31:59.179632Z",
     "shell.execute_reply": "2021-06-24T11:31:59.180338Z"
    }
   },
   "outputs": [
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      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
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     },
     "metadata": {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "fig, ax = plt.subplots(figsize=[5, 5])\n",
    "op.topotools.plot_coordinates(network=combo_net, c=Deff['pore.concentration'], \n",
    "                              cmap='jet', markersize=40, ax=ax);"
   ]
  }
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